Payne is the Knicks' first coaching addition since they officially named Thibodeau as their new bench boss July 30.
"I'm thrilled that Kenny has joined my staff as an assistant coach," Thibodeau said in a statement. "He has an outstanding ability to forge relationships with players and improve their skills.
"He knows what it takes to win and has learned from one of the best coaches there is in John Calipari. Kenny will be a tremendous addition to our organization."
Payne joined Calipari's staff in 2010 as an assistant before being promoted to associate head coach in 2014. During his time with the Wildcats, Payne helped recruit several players who would go on to become NBA stars, including Anthony Davis and Karl-Anthony Towns. He also played a role in Kentucky's national championship in 2012.
"I am a better coach and leader of young men today because of my time in Lexington under the legendary Coach Cal," Payne said. "I now take the next step in my basketball journey and fulfill my dream of coaching in the NBA.
"I'm beyond grateful and excited for the chance to work for such a prestigious organization as the New York Knicks under the leadership of Leon Rose, Scott Perry, William Wesley, and Tom Thibodeau, who I have such great admiration and respect for."